Waveguide structure and printed-circuit board

ABSTRACT

A waveguide structure or a printed-circuit board is formed using a plurality of unit structures which are repetitively aligned in a one-dimensional manner or in a two-dimensional manner. The unit structure includes first and second conductive planes which are disposed in parallel with each other, a transmission line having an open end which is formed in a layer different from the first and second conductive planes and positioned to face the second conductive plane, and a conductive via electrically connecting the transmission line to the first conductive plane.

The present application is a Divisional Application of U.S. PatentApplication No. 12/457,801, filed on Jun. 22, 2009.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to waveguide structures for use inpropagation of electromagnetic waves such as microwaves and millimeterwaves, and in particular to electromagnetic-band-gap (EBG) structuresfor suppressing propagation of electromagnetic waves in specificfrequency bands. The present invention also relates to printed-circuitboards including waveguide structures.

The present application claims priority on Japanese Patent ApplicationNo. 2008-164338, the content of which is incorporated herein byreference.

2. Description of Related Art

Various technologies regarding waveguide structures and printed-circuitboards for suppressing propagation of electromagnetic waves in specificfrequency bands have been developed and disclosed in various documents.[0006] Patent Document 1: U.S. Patent Application Publication, US2005/019051 A1 [0007] Patent Document 2: U.S. Patent ApplicationPublication, US 2005/0205292 A1

Recently, methods for artificially controlling frequency dispersions ofelectromagnetic waves by use of repetitively aligned conductive patcheshave been provided. Among those structures, structures having band gapsin frequency dispersions are referred to as EBG structures, which areexpectedly applied to filters for suppressing propagation of unwantednoise in printed-circuit boards or substrates of device packages.

Patent Document 1 teaches an EBG structure for reducing noisepropagation between parallel plates. The EBG structure includesconductive patches, which are aligned in a third layer between parallelplates and which serve as capacitances for one conductive plane of theparallel plates, and admittances (or shunts) for connecting theconductive patches to another conductive plane of the parallel plates,wherein the admittances are repetitively aligned in a one-dimensionalmanner or a two-dimensional manner along the parallel plates. Due toband gaps occurring in frequency bands in which the admittances serve asinductances in the EBG structure, it is possible to set band gaps bycontrolling serial-LC resonance frequencies of admittances.

Securing adequate capacitances and inductances in the above EBGstructure leads to increasing the areas of conductive patches orincreasing the lengths of conductive vias, which in turn makes itdifficult to reduce the sizes of structures.

Patent Document 2 teaches a structure in which chip capacitors aremounted on the surface and are connected in parallel between conductiveplanes and conductive patches. This structure increases capacitanceswithout increasing the areas of conductive patches.

However, Patent Document 2 discloses that using chip capacitorsincreases the number of parts so as to increase the manufacturing cost.

In the above circumstances, the inventor has recognized that it isnecessary to fabricate an EBG structure (or a waveguide structure) and aprinted-circuit board with a reduced size, without using chipcomponents, and with low manufacturing cost.

SUMMARY

The present invention seeks to solve the above problem, or to improveupon the problem at least in part.

The present invention is directed to a structure or a printed-circuitboard, which includes a plurality of unit structures repetitivelyaligned in a one-dimensional manner or a two-dimensional manner.

In a first embodiment, the unit structure includes first and secondconductive planes which are disposed in parallel with each other, atransmission line having an open end which is formed in a layerdifferent from the first and second conductive planes and positioned toface the second conductive plane, and a conductive via electricallyconnecting the transmission line to the first conductive plane.

In a second embodiment, the unit structure includes first and secondconductive planes which are disposed in parallel with each other, afirst transmission line laid on a first plane which is positionedbetween the first and second conductive planes so as to face the secondconductive plane, a second transmission line having an open end laid ona second plane which is positioned to face the second conductive planeoutside a region circumscribed between the first and second conductiveplanes, a first conductive via electrically connecting the firsttransmission line to the first conductive plane, and a second conductivevia electrically connecting the first transmission line to the secondtransmission line. In addition, a clearance is formed at a prescribedposition corresponding to the second conductive in the second conductiveplane, thus electrically isolating the second conductive plane from thesecond conductive via.

In a third embodiment, the unit structure includes first and secondconductive planes which are disposed in parallel with each other, afirst transmission line having an open end which is formed in a firstplane different from the first and second conductive planes andpositioned to face the first conductive plane, a second transmissionline having an open end which is formed in a second plane different fromthe first and second conductive planes and positioned to face the secondconductive plane, and a conductive via electrically connecting the firsttransmission line to the second transmission line.

In a fourth embodiment, the unit structure includes first and secondconductive planes which are disposed in parallel with each other, afirst transmission line which is formed in a first plane positionedbetween the first and second conductive planes so as to face the secondconductive plane, a second transmission line having an open end which isformed in a second plane positioned to face the second conductive planeoutside a region circumscribed between the first and second conductiveplanes, a third transmission line which is formed in a third planepositioned between the first conductive plane and the first transmissionline so as to face the first conductive plane, a fourth transmissionline having an open end which is formed in a fourth plane positioned toface the first conductive plane outside a region circumscribed betweenthe first and second conductive planes, a first conductive viaelectrically connecting the first transmission line to the thirdtransmission line, a second conductive via electrically connecting thefirst transmission line to the second transmission line, and a thirdconductive via electrically connecting the third transmission line tothe fourth transmission line. In addition, a first clearance is formedat a first position corresponding to the third conductive via in thefirst conductive plane, which is thus electrically isolated from thethird conductive via. Furthermore, a second clearance is formed at asecond position corresponding to the second conductive via in the secondconductive plane, which is thus electrically isolated from the secondconductive via.

In a fifth embodiment, the unit structure includes first and secondconductive planes which are disposed in parallel with each other, afirst transmission line having an open end which is formed in a firstplane different from the first and second conductive planes andpositioned to face the first conductive plane, a second transmissionline having an open end which is formed in a second plane different fromthe first and second conductive planes so as to face the secondconductive plane, a first conductive via electrically connecting thesecond transmission line to the first conductive plane, and a secondconductive via electrically connecting the first conductive plane to thesecond conductive plane. In addition, a first clearance is formed at afirst position corresponding to the second conductive via in the firstconductive plane, which is thus electrically isolated from the secondconductive via. Furthermore, a second clearance is formed at a secondposition corresponding to the first conductive via in the secondconductive plane, which is thus electrically isolated from the firstconductive via.

BRIEF DESCRIPTION OF THE DRAWINGS

The above features and advantages of the present invention will be moreapparent from the following description of certain preferred embodimentstaken in conjunction with the accompanying drawings, in which:

FIG. 1 is a cross-sectional view of an EBG structure used for explaininga waveguide structure according to a first embodiment of the presentinvention;

FIG. 2 is a plan view of the EBG structure corresponding to thewaveguide structure of the first embodiment;

FIG. 3 is a circuit diagram showing an equivalent circuit of the EBGstructure;

FIG. 4 is a graph plotting the imaginary part of admittance in the EBGstructure;

FIG. 5 is a graph showing calculation results regarding insertion lossin propagation of electromagnetic waves through the EBG structure;

FIG. 6 is a cross-sectional view showing an EBG structure including anadditional dielectric layer deposited above transmission lines;

FIG. 7A is a plan view showing spiral-shaped transmission lines;

FIG. 7B is a plan view showing meandering transmission lines;

FIG. 8 is a plan view showing an EBG structure in which transmissionlines are aligned to detour around a component X;

FIG. 9 is a cross-sectional view of an EBG structure used for explaininga waveguide structure according to a second embodiment of the presentinvention;

FIG. 10 is a cross-sectional view showing a variation of the EBGstructure shown in FIG. 9;

FIG. 11 is a cross-sectional view of an EBG structure used forexplaining a waveguide structure according to a third embodiment of thepresent invention;

FIG. 12 is a cross-sectional view showing a variation of the EBGstructure shown in FIG. 11;

FIG. 13 is a cross-sectional view of an EBG structure used forexplaining a waveguide structure according to a fourth embodiment of thepresent invention;

FIG. 14 is a circuit diagram showing an equivalent circuit of the EBGstructure shown in FIG. 13;

FIG. 15 is a cross-sectional view showing a first variation of thefourth embodiment which is created based on the EBG structure of thesecond embodiment;

FIG. 16 is a cross-sectional view showing a second variation of thefourth embodiment which is created based on the EBG structure of thethird embodiment;

FIG. 17 is a cross-sectional view of an EBG structure used forexplaining a waveguide structure according to a fifth embodiment of thepresent invention;

FIG. 18 is a plan view of the EBG structure shown in FIG. 17;

FIG. 19 is a cross-sectional view showing a variation of the fifthembodiment which is crated based on the EBG structure shown in FIG. 15;

FIG. 20 is a plan view showing another variation of the fifth embodimentincluding spiral-shaped transmission lines;

FIG. 21 is a plan view showing a printed-circuit board incorporating theEBG structure according to a sixth embodiment of the present invention;

FIG. 22 is a cross-sectional view of the printed-circuit board shown inFIG. 21;

FIG. 23 is a plan view showing a variation of the sixth embodiment;

FIG. 24 is a plan view showing a printed-circuit board according to aseventh embodiment of the present invention;

FIG. 25 is a plan view showing a first variation of the seventhembodiment in which two types of EBG structures are alternately alignedin the noise propagation direction; and

FIG. 26 is a plan view showing a second variation of the seventhembodiment in which two types of EBG structures are aligned in acheckered pattern.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present invention will be now described herein with reference toillustrative embodiments. Those skilled in the art will recognize thatmany alternative embodiments can be accomplished using the teachings ofthe present invention and that the invention is not limited to theembodiments illustrated for explanatory purposes.

In the following description regarding waveguide structures andprinted-circuit boards according to the present invention with referenceto the accompanying drawings, a vertical direction in FIG. 1 will bereferred to as a thickness direction of a board.

1. First Embodiment

FIG. 1 is a cross-sectional view of an EBG structure according to afirst embodiment. FIG. 2 is a plan view of the EBG structure, so thatFIG. 1 is a cross-sectional view taken along line A-A in FIG. 1.

The EBG structure (or the waveguide structure) of the first embodimentis a parallel-plate conductive structure; as shown in FIG. 1, itincludes first and second conductive planes 1 and 2, which are alignedin parallel with a distance therebetween in the thickness direction, aswell as a unit structure 3. The unit structure 3 includes a transmissionline 4, which is laid in a layer different from the layers of the firstand second planes 1 and 2, and a conductive via 5 for electricallyconnecting the transmission line 4 and the first conductive plane 1.

Specifically, the EBG structure includes a first dielectric layer 6, anda second dielectric layer 7 which is deposited on an upper surface ofthe first dielectric layer 6 in the thickness direction, wherein thefirst conductive plane 1 is disposed on a lower surface of the firstdielectric layer 6 in the thickness direction, and the second conductiveplane 2 is disposed between the first dielectric layer 6 and the seconddielectric layer 7. The conductive via 5 is elongated in the thicknessdirection from the upper surface of the second conductive plane 2 to thelower surface of the first conductive plane 1. The transmission line 4is disposed on the upper surface of the second dielectric layer 7 in thethickness direction. That is, the transmission line 4 is disposed toface the first conductive plane 1 in the thickness direction withrespect to the second conductive plane 2.

The transmission line 4 uses the second conductive plane 2 as a returnpath, wherein one end thereof (i.e. a right-side end in FIG. 1) servesas an open end so that the transmission line 4 serves as an open stub.The other end of the transmission line 4 (i.e. a left-side end inFIG. 1) is electrically connected to a pad 8 which is formed in the sameplane as the transmission line 4 and which is electrically connected tothe first conductive plane 1 via the conductive via 5 elongated in thethickness direction. The second conductive plane 2 is equipped with aclearance 9 which overlaps with the conductive via 5 in position, sothat the conductive via 5 is electrically isolated from and is notbrought into contact with the second conductive plane 2 by means of theclearance 9.

In the above EGB structure, the transmission line 4, the conductive via5, and the pad 8 are devoted to an admittance, which is combined withthe clearance 9 so as to form the unit structure 3. One or more unitstructures 3 are repetitively aligned at a lattice point defined by anindependent vector A=(A1,A2) and B=(B1,B2) on the X-Y plane. The firstembodiment exemplarily refers to a tetragonal lattice defined by A=(a,0)and B=(0,a) shown in FIG. 2 as a basic-mode lattice point. In the firstembodiment, the transmission line 4 is inclined to the tetragonallattice of A=(a,0) and B=(0,a) by a certain angle, wherein it ispossible to secure a long length d with respect to the transmission line4 without interfering with the clearance 9 in its periphery. Strictlyspeaking, the transmission line 4 is not included in the cross sectiontaken along line A-A in FIG. 2; for the sake of convenience, thetransmission lines 4 are illustrated using dotted lines in FIG. 1. Forthe sake of convenience, FIG. 2 shows the second conductive plane 2 viathe perspective scope of the second dielectric layer 7.

Next, a basic operating principle of the above EBG structure will bedescribed.

FIG. 3 shows an equivalent circuit along the X-axis or Y-axis in FIG. 2.FIG. 4 is a graph for plotting the imaginary part of a paralleladmittance. FIG. 5 is a graph showing calculation results regarding aninsertion loss in propagation of electromagnetic waves through the EBGstructure of the first embodiment.

Each repetitive unit 10 of the equivalent circuit shown in FIG. 3 isconstituted of a serial impedance 11 and a parallel admittance 12. Theserial impedance includes an inductance 13 formed between the first andsecond conductive planes 1 and 2. The parallel admittance 12 includes acapacitance 14 formed between the first and second conductive planes 1and 2, an inductance 15 of the conductive via 5, and the transmissionlines 4. The overall equivalent circuit of the EBG structure is formedby repetitively connecting one or more repetitive units 10.

In the EBG structure, band gaps occur in frequency bands in which theparallel admittances 12 serve as inductances. An admittance Yrepresentative of the parallel admittance 12 is given by equation (1).

$\begin{matrix}{Y = {\frac{1}{Z_{i\; n} + {\; \omega \; L_{via}}} + {\; \omega \; C_{plane}}}} & (1)\end{matrix}$

Y: Admittance

Z_(in): Input impedance of the transmission line 4 in view of the pad 8

ω: Angular frequency

L_(via): Inductance

C_(plane): Capacitance

The input impedance Z_(in) of the transmission line 4 in view of the pad8 is given by equation (2).

$\begin{matrix}{{Z_{i\; n} = {Z_{0} \times \frac{Z_{T} + {\; Z_{0}{\tan \left( {\beta \; d} \right)}}}{Z_{0} + {\; Z_{T}{\tan \left( {\beta \; d} \right)}}}}}{\beta = {\omega \sqrt{ɛ_{eff}ɛ_{0}\mu_{0}}}}} & (2)\end{matrix}$

Z_(i)n: Input impedance of the transmission line 4 in view of the pad 8

Z₀: Characteristic impedance

Z_(T): Terminating resistance

d: Length of the transmission line

ω: Angular frequency

ε_(eff): Effective dielectric constant

ε₀: Dielectric constant of a vacuum

μ₀: Magnetic permeability of a vacuum

FIG. 4 shows frequency-dependent impedance curves 16 based on theimaginary part of the admittance Y calculated by equations (1) and (2)using parameters such as the capacitance 14 of 0.73 pF, the inductance15 of 0.22 nH, the characteristic impedance of 20.25Ω of thetransmission line 4, the length d=7.5 mm of the transmission line 4, andthe effective dielectric constant ε_(eff)=3.47 of the transmission line4. The transmission line 4 is of an open-end type so that theterminating resistance Z_(T) thereof is presumed to be infinite. Due toan impedance-converting effect of the transmission line 4, thecapacitive property (where Im(Y)>0) and the inductive property (whereIm(Y)<0) alternately emerge in the impedance Im(Y) based on theadmittance Y. In FIG. 4, the impedance Im(Y) becomes negative infrequency bands 17, thus showing the inductive property. For thisreason, it is anticipated that band gaps may likely occur in thefrequency bands 17.

When Equation (1) is modified to represent the function of length d ofthe transmission line by way of substitution in Equation (2), and byletting Z_(T) to approach infinity as described above, the waveguidestructure is thereby configured to suppress electromagnetic propagationbetween a power source and a ground plane at a frequency f satisfying aninequality Im(Y(f))≦0, where Im(Y(f)) is an imaginary component of aparallel admittance Y(f) defined as:

${Y(f)} = {\frac{1}{\left( {{2\pi \; {fL}_{via}} - \frac{Z_{0}}{\tan \left( {2\pi \; f\sqrt{ɛ_{eff}ɛ_{0}\mu_{0}}d} \right)}} \right)} + {\; 2\pi \; {fC}_{plane}}}$

where f denotes frequency, i denotes an imaginary component meaning thati²=−1, L_(via) denotes an inductance of the conductive via, C_(plane)denotes a capacitance between the power source and the ground plane, Z₀denotes a characteristic impedance of the transmission line, d denotes alength of the transmission line, ε_(eff) denotes an effective dielectricconstant, ε₀ denotes a dielectric constant under vacuum, and μ₀ denotesa magnetic permeability under vacuum.

In the EBG structure, a physical structure corresponding to therepetitive unit 10 of the equivalent circuit is repetitively aligned atthe lattice point defined by a certain lattice distance “a” on the X-Yplane. Due to a repetitive boundary condition imposed on the repetitiveunit 10 of the equivalent circuit shown in FIG. 3, it is necessary tocalculate band gaps in consideration of the structural repetitiveness.FIG. 5 shows calculation results regarding an insertion loss (S21) inpropagation of electromagnetic waves through the EBG structure by adistance of 7×a. A dotted curve 18 shown in FIG. 5 shows the calculationresult which is produced by imposing the repetitive boundary conditionon the repetitive unit 10 of the equivalent circuit while using the sameparameters of circuit components used for producing calculation resultsof FIG. 4. A solid curve 19 shown in FIG. 5 shows the result ofnumerical calculation by way of three-dimensional electromagneticanalysis. A model subjected to electromagnetic analysis is designed withprescribed structural dimensions, such as the thickness t=400 μm of thefirst dielectric layer 6, the thickness h=60 μm of the second dielectriclayer 7, the width b=300 μm of the conductive via 5, and the lengthd=7.5 mm of the transmission line 4. FIG. 5 shows that calculated bandgaps of the equivalent circuit significantly match the result ofelectromagnetic analysis.

Calculated frequency bands of band gaps shown in FIG. 5 significantlymatch the frequency bands 17 shown in FIG. 4. This indicates thatfrequency bands of band gaps occurring in the EBG structure can beapproximately illustrated by frequency characteristics of admittances.Since the admittance Y of the parallel admittance 12 is determined byequations (1) and (2), it is possible to bring band gaps into desiredfrequency bands by appropriately setting parameters of these equations.In particular, the length d of the transmission line 4 has a relativelyhigh degree of freedom in designing; hence, it is possible to easilycontrol band gaps by varying the length d. Frequencies of band gaps canbe lowered by increasing the length d of the transmission line 4 butwithout necessarily changing its area; hence, it is possible to reducethe mounting area of the EBG structure. Since the EBG structure does notneed chip components, it is possible to reduce the manufacturing cost incomparison with the conventional arts.

First embodiment of FIG. 1 shows that no structure exists above thetransmission lines 4, whereas it is possible to modify it such that acertain structure is mounted on the transmission lines 4. As shown inFIG. 6, for example, it is possible to arrange an additional dielectriclayer (i.e. a third dielectric layer 20) above the transmission lines 4,thus increasing the effective dielectric constant of the transmissionline 4. Equation (2) indicates that the impedance converting effectappears markedly on the transmission line 4 as the effective dielectricconstant of the transmission line 4 becomes higher; hence, it ispossible to lower the frequencies of band gaps without increasing thelength d of the transmission line 4. For lowering frequencies of bandgaps, it is preferable to use a dielectric material having a highdielectric constant for the third dielectric layer 20. Since it isunnecessary to lower the frequencies of band gaps, it is possible to useany type of dielectric materials for additional dielectric layersdeposited above the transmission lines 4.

As long as one end of the transmission line 4 serves as an open endwhile the other end is connected to the pad 8, it is possible to employany type of arrangements and shapes to the transmission lines 4, whichdo not affect the inherent property of the present invention.

In the first embodiment, as shown in FIG. 2, the transmission lines 4are inclined to the X-axis and Y-axis with certain angles therebetweenso as not to interfere with the clearances 9 in their periphery, whereasthey can be aligned in parallel with the X-axis and Y-axis withoutinterference with the clearances 9. Although the first embodiment isdesigned such that the transmission lines 4 are linearly elongated asshown in FIG. 2, it is possible to employ the spiral shapes shown inFIG. 7A or the meandering shapes shown in FIG. 7B, for example. Theseexamples adequately secure the length d of the transmission line 4within a small mounting area.

The transmission lines 4 are not necessarily aligned with the samearrangement and the same shapes shown in FIG. 2 in connection with allthe unit structures 3. For example, it is possible to align thetransmission lines 4 while avoiding a component X mounted on the surfaceas shown in FIG. 8, thus securing high-density packaging.

FIG. 2 shows the tetragonal lattice as the lattice point forrepetitively aligning the unit structure 3; but this is not arestriction. For example, it is possible to employ triangular latticesor a one-dimensional repetitive alignment, thus demonstratingsatisfactory effects.

For the sake of convenience in manufacturing, the pads 8 are aligned inconnection with the transmission lines 4 and the conductive vias 5,whereas it is possible to modify the EBG structure not including thepads 8 without affecting the inherent properties of the presentinvention.

2. Second Embodiment

Next, a waveguide structure according to a second embodiment of thepresent invention will be described with reference to FIG. 9.

FIG. 9 is a cross-sectional view showing an EBG structure according tothe second embodiment.

The EBG structure of the second embodiment is a variation of the EBGstructure of the first embodiment, wherein parts identical to those ofthe first embodiment are designated by the same reference numerals, thusavoiding duplicate descriptions thereof.

The EGB structure of the second embodiment shown in FIG. 9 ischaracterized in that a transmission line 4 is embedded inside theregion sandwiched between the first conductive plane 1 and the secondconductive plane 2. Specifically, the first conductive plane 1 isattached to the lower surface of the first dielectric layer 6 in itsthickness direction while the second conductive plane 2 is attached tothe upper surface of the second dielectric layer 7 in its thicknessdirection in the EBG structure of the second embodiment. Thetransmission line 104 which uses the second conductive plane 2 as areturn path is laid in the intermediate layer circumscribed between thefirst dielectric layer 6 and the second dielectric layer 7.

Similar to the transmission line 4 for use in the first embodiment, oneend of the transmission line 104 is an open end, thus serving as an openstub. The other end of the transmission line 104 is connected to the pad8 which is positioned in the same plane as the transmission line 104,wherein the pad 8 is electrically connected to the first conductiveplane 1 via a conductive via 105. Similar to the first embodiment, thepad 8, the transmission line 104, and the conductive via 105 serve as anadmittance, which is combined with the clearance arranged for the secondconductive plane 2 so as to form the unit structure 3. The arrangementof the unit structure 3 as well as the arrangement and shape of thetransmission line 104 employed in the second embodiment are similar tothose employed in the first embodiment.

Since the transmission line 104 is shielded by the first and secondconductive planes 1 and 2 in the EBG structure of the second embodiment,it is possible to reduce the number of unwanted electromagnetic wavesbeing emitted from the transmission line 104 to the exterior surface.

FIG. 9 shows the second embodiment in which the conductive via 105 is athrough-via; but this is not a restriction as long as the pad 8 iselectrically connected to the first conductive plane 1. As shown in FIG.10, for example, it is possible to arrange a conductive via 105_X of anon-through-via type without affecting the property of the presentinvention. Since the EBG structure shown in FIG. 10 does not need theclearance 9 for the second conductive plane 2, it is possible toeliminate electromagnetic waves from being emitted from the clearance 9to the exterior surface.

3. Third Embodiment

Next, a waveguide structure according to a third embodiment of thepresent invention will be described with reference to FIG. 11.

FIG. 11 is a cross-sectional view showing an EBG structure according tothe third embodiment.

The EBG structure of the third embodiment is a variation of the EBGstructure of the second embodiment, wherein parts identical to those ofthe second embodiment are designated by the same reference numerals,thus avoiding duplicate descriptions thereof.

The EBG structure of the third embodiment shown in FIG. 11 is formedusing a unit structure 203 including a first transmission line 204A laidbetween the first conductive plane 1 and the second conductive plane 2,a second transmission line 204B positioned to face the second conductiveplane 2 with respect to the first conductive plane 1, a first conductivevia 205A for electrically connecting one end of the first transmissionline 204A (i.e. a left-side end in FIG. 11) to the first conductiveplane 1, and a second conductive via 205B for electrically connectingthe other end of the first transmission line 204A (i.e. a right-side endin FIG. 11) to the second transmission line 204B.

Similar to the second embodiment, the third embodiment is designed suchthat the first conductive plane 1 is attached to the lower surface ofthe first dielectric layer 6 in its thickness direction while the secondconductive plane 2 is attached to the upper surface of the seconddielectric layer 7 in its thickness direction. A third dielectric layer(i.e. a surface dielectric layer 220) for covering the second conductiveplane 2 is deposited on the upper surface of the second dielectric layer7. The first transmission line 204A is aligned at the position of thetransmission line 104 used in the second embodiment (i.e. the positionbetween the first dielectric layer 6 and the second dielectric layer 7),while the second transmission line 204B whose one end is an open end isaligned on the upper surface of the surface dielectric layer 220 in itsthickness direction. The first transmission line 204A uses the secondconductive plane 2 as a return path, wherein pads 8A and 8B which arealigned in the same plane as the first transmission line 204A areelectrically connected to the opposite ends of the first transmissionline 204A. The second transmission line 204B uses the second conductiveplane 2 as a return path, wherein one end of the second transmissionline 204B is an open end, thus serving as an open stub. The other end ofthe second transmission line 204B is electrically connected to the pad 8which is aligned in the same plane as the second transmission line 204B.

The pad 8A attached to the first transmission line 204A is electricallyconnected to the first conductive plane 1 via a first conductive via205A which is elongated in the thickness direction. The pad 8B attachedto the first transmission line 204A is electrically connected to the pad8 attached to the second transmission line 204B via a second conductivevia 205B which is elongated in the thickness direction. The clearance 9is arranged for the second conductive plane 2 in connection with thesecond conductive via 205B, so that the second conductive plane 2 iselectrically isolated from and is prevented from contacting the secondconductive via 205B by means of the clearance 9.

Since the first transmission line 204A laid in the intermediate layerand the second transmission line 204B laid in the surface layercollectively serve as an open stub in the EBG structure of the thirdembodiment, it is possible to secure an adequate transmission-linelength d within a small area in packaging.

Similar to the first and second embodiments, various patterns can becreated in terms of the arrangement and shapes of the first and secondtransmission lines 204A and 204B. It is possible to employ spiral shapesor meandering shapes, for example. Thus, it is possible to produce theEBG structure which can be mounted on a small area in packaging.

FIG. 11 shows the third embodiment in which both the first and secondconductive vias 205A and 205B are of a non-through-via type, whereas itis possible to use through vias. As shown in FIG. 12, for example, it ispossible to replace the second conductive via 205B with another secondconductive via 205B_X serving as a through via. In the EBG structureshown in FIG. 12, the clearance 9 is formed at a prescribed positioncorresponding to the second conductive via 205B_X in relation to thefirst conductive plane 1, thus preventing the first conductive plane 1from being electrically connected to the second conductive plane 2. Inaddition, it is possible to use a through via as the first conductivevia 205A.

4. Fourth Embodiment

Next, a waveguide structure according to a fourth embodiment of thepresent invention will be described with reference to FIG. 13.

FIG. 13 is a cross-sectional view showing an EBG structure according tothe fourth embodiment.

The EBG structure of the fourth embodiment is a variation of the EBGstructure of the first embodiment, wherein parts identical to those usedin the first embodiment are designated by the same reference numerals,thus avoiding duplicate descriptions thereof.

In contrast to the EBG structure of the first, second, and thirdembodiments in which the transmission lines 4, 104, 204A, and 204B arealigned in proximity to only the second conductive plane 2 within thefirst and second conductive planes 1 and 2 and are each configured touse the second conductive plane 2 as a return path, the fourthembodiment is characterized in that transmission lines 304A and 304B arearranged for the first and second conductive planes 1 and 2respectively. That is, the EBG structure of the fourth embodiment isminor-plane symmetrical to the EBG structure of the first embodiment inthe vertical direction. As shown in FIG. 13, it is formed using a unitstructure 303 including the first transmission line 304A which is laidin the layer different from the layers of the first and secondconductive planes 1 and 2 and which uses the first conductive plane 1 asa return path, the second transmission line 304B which is laid in thelayer different from the layers of the first and second conductiveplanes 1 and 2 and which uses the second conductive plane 2 as a returnpath, and a conductive via 305 for electrically connecting theprescribed ends of the transmission lines 304A and 304B together.

Specifically, the fourth embodiment is designed in such a manner similarto the first embodiment that the first conductive plane 1 is aligned onthe lower surface of the first dielectric layer 6 in its thicknessdirection while the second conductive plane 2 is inserted between thefirst dielectric layer 6 and the second dielectric layer 7. A thirddielectric layer (i.e. a backside dielectric layer 320) for covering thefirst conductive plane 1 is deposited on the lower surface of the firstdielectric layer 6 in its thickness direction. In addition, the firsttransmission line 304A is aligned on the lower surface of the backsidedielectric layer 320 in its thickness direction, while the secondtransmission line 304B is aligned on the surface of the seconddielectric layer 7 in its thickness direction. That is, the first andsecond transmission lines 304A and 304B are positioned outside theregion sandwiched between the first and second conductive planes 1 and2.

Open ends are formed at one end of the first transmission line 304A(i.e. a right-side end in FIG. 13) and one end of the secondtransmission line 304B, so that the first and second transmission lines304A and 304B serve as open stubs. The pads 8 which are formed in thesame planes as the first and second transmission lines 304A and 304B areelectrically connected to the other end of the first transmission line304A (i.e. a left-side end in FIG. 13) and the other end of the secondtransmission line 304B. The pad 8 attached to the first transmissionline 304A is electrically connected to the pad 8 attached to the secondtransmission line 304B via a conductive via 305 which is elongated inthe thickness direction. The clearances 9 are formed at the positionscorresponding to the opposite ends of the conductive via 305 inproximity to the first and second conductive planes 1 and 2, which arethus electrically isolated from each other and are not brought intocontact with each other via the clearances 9.

FIG. 14 is a circuit diagram showing an equivalent circuit of the EBGstructure of the fourth embodiment.

A repetitive unit 310 of the equivalent circuit shown in FIG. 14 isconstituted of a serial impedance 311 and a parallel admittance 312.Similar to the first embodiment, the serial impedance 311 is composed ofan inductance 13 formed between the first and second conductive planes 1and 2. The parallel admittance 312 is constituted of a capacitance 314formed between the first and second conductive planes 1 and 2, and aninductance 315 of the conductive via 305, as well as the first andsecond transmission lines 304A and 304B. The parallel admittance 312used in the fourth embodiment is designed such that the open stub of thesecond transmission line 304B is additionally connected in series withthe parallel admittance 12 used in the first embodiment. Similar to thefirst embodiment, the fourth embodiment is characterized in that bandgaps occur in frequency bands in which the parallel admittance 312becomes negative.

The EBG structure of the fourth embodiment is minor-plane symmetrical tothe EBG structure of the first embodiment in the vertical direction.Instead, it can be reconfigured in a manner minor-plane symmetrical tothe EBG structure of the second or third embodiment in the verticaldirection.

Specifically, it is possible to create an EBG structure shown in FIG. 15based on the EBG structure of the second embodiment, wherein a thirddielectric layer 120 is inserted between the first conductive plane 1and the first dielectric layer 6; a first transmission line 104A whichuses the first conductive plane 1 as a return path is aligned betweenthe first dielectric layer 6 and the third dielectric layer 120; and asecond transmission line 104B which uses the second conductive plane 2as a return path is aligned between the first dielectric layer 6 and thesecond dielectric layer 7. Open ends are formed at one end of the firsttransmission line 104A and one end of the second transmission line 104B,while the pads 8 are electrically connected to the other ends of thetransmission lines 104A and 104B. The pads 8 attached to the first andsecond transmission lines 104A and 104B are electrically connectedtogether via a conductive via 105_X of a non-through-via type.

It is possible to create an EBG structure shown in FIG. 16 based on theEBG structure of the third embodiment, wherein a third dielectric layer320A is inserted between the first conductive plane 1 and the firstdielectric layer 6, and a backside dielectric layer 320B for coveringthe first conductive plane 1 is deposited on the lower surface of thethird dielectric layer 320A in its thickness direction. In addition, athird transmission line 204C which uses the first conductive plane 1 asa return path is laid between the first conductive plane 1 and the firsttransmission line 204A, in other words, between the first dielectriclayer 6 and the third dielectric layer 320A. Furthermore, a fourthtransmission line 204D which uses the first conductive plane 1 as areturn path is positioned to face the first conductive plane 1 outside aregion circumscribed between the first conductive plane 1 and the secondconductive plane 2, in other words, it is aligned on the lower surfaceof the backside dielectric layer 320B in its thickness direction. Thepads 8A and 8B which are formed in the same plane as the thirdtransmission line 204C are electrically connected to the opposite endsof the third transmission line 204C. One end of the fourth transmissionline 204D is an open end, and the pad 8 which is formed in the sameplane as the fourth transmission line 204D is electrically connected tothe other end of the fourth transmission line 204D.

The pad 8A attached to the first transmission line 204A is electricallyconnected to the pad 8A attached to the third transmission line 204C viathe first conductive via 205A which is elongated in the thicknessdirection. The pad 8B attached to the third transmission line 204C iselectrically connected to the pad 8 attached to the fourth transmissionline 204D via a third conductive via 205C which is elongated in thethickness direction. The clearance 9 is formed at a prescribed positioncorresponding to the third conductive via 205C in proximity to the firstconductive plane 1; hence, the first conductive plane 1 is electricallyisolated from and is prevented from contacting the third conductive via205C by means of the clearance 9.

All the EBG structures shown in FIGS. 13, 15, and 16 are designed in amirror-plane symmetrical manner in the vertical direction; but this isnot a restriction. It is possible to create an asymmetrical structure inwhich the first transmission line 304A has a linear shape while thesecond transmission line 304B has a spiral shape, for example. It ispossible to make the second dielectric layer 7 differ from the backsidedielectric layer 320 in thickness. In this case, it is noticed that theeffective dielectric constant of the first transmission line 304A shoulddiffer from the effective dielectric constant of the second transmissionline 304B.

5. Fifth Embodiment

Next, a waveguide structure according to a fifth embodiment of thepresent invention will be described with reference to FIGS. 17 and 18.

FIG. 17 is a cross-sectional view of an EBG structure according to thefifth embodiment. FIG. 18 is a plan view of the EBG structure, so thatFIG. 17 is a cross-sectional view taken along line B-B in FIG. 17.

The EBG structure of the fifth embodiment is a variation of the EBGstructure of the fourth embodiment, wherein parts identical to those ofthe fourth embodiment are designated by the same reference numerals,thus avoiding duplicate descriptions thereof.

In contrast to the EBG structure of the fourth embodiment shown in FIG.13 in which the first transmission line 304A which uses the firstconductive plane 1 as a return path is electrically connected to thesecond transmission line 304B which uses the second conductive plane 2as a return path via the conductive via 305, the EBG structure of thefifth embodiment shown in FIG. 17 is designed such that the secondtransmission line 304B which uses the second conductive plane 2 as areturn path is electrically connected to the first conductive plane 1via a first conductive via 405A, while the first transmission line 304Awhich uses the first conductive plane 1 as a return path is electricallyconnected to the second conductive plane 2 as a second conductive via405B. That is, the fifth embodiment is formed using a unit structure 403including the first conductive via 405A for electrically connecting thefirst conductive plane 1 to the second transmission line 304B, and thesecond conductive via 405B for electrically connecting the secondconductive plane 2 to the first transmission line 304A.

Specifically, the fifth embodiment is designed in such a manner similarto the fourth embodiment that the backside dielectric layer 320 isdeposited on the lower surface of the first dielectric layer 6 in itsthickness direction; the first conductive plane 1 is inserted betweenthe first dielectric layer 6 and the backside dielectric layer 320; andthe second conductive plane 2 is inserted between the first dielectriclayer 6 and the second dielectric layer 7.

In addition, the first transmission line 304A is aligned on the lowersurface of the backside dielectric layer 320 in its thickness direction,while the second transmission line 304B is aligned on the upper surfaceof the second dielectric layer 7 in its thickness direction.

The pads 8 are electrically connected to the left-side ends of the firstand second transmission lines 304A and 304B. In a plan view, the pad 8attached to the first transmission line 304A is shifted in position fromthe pad 8 attached to the second transmission line 304B. In addition,the pad 8 attached to the second transmission line 304B is electricallyconnected to the first conductive plane 1 via the first conductive via405A, while the pad 8 attached to the first transmission line 304A iselectrically connected to the second conductive plane 2. That is, afirst admittance is formed by the first transmission line 304A, the pad8, and the second conductive via 405B, while a second admittance isformed by the second transmission line 304B, the pad 8, and the firstconductive via 405A. In a plan view of FIG. 18, the second admittance isformed at the position corresponding the first admittance subjected toparallel translation by A/2+B/2=(a/2,a/2) and further subjected tovertical inversion on the X-Y plane.

The EBG structure of the fifth embodiment makes it possible to locatethe admittances with a high density in a plan view of FIG. 18; hence, itis possible to reduce the area of the EBG structure in packaging.

The EBG structure of the fifth embodiment is a variation of the EBGstructure shown in FIG. 13, wherein it can be modified in a mannersimilar to the EBG structure shown in FIG. 15.

Specifically, the EBG structure shown in FIG. 19 is created based on theEBG structure shown in FIG. 15, wherein the second transmission line104B which uses the second conductive plane 2 as a return path iselectrically connected to the first conductive plane 1 via a firstconductive via 105A, and the first transmission line 104A which uses thefirst conductive plane 1 as a return path is electrically connected tothe second conductive plane 2 via a second conductive via 105B.

In addition, it is possible to create an asymmetrical structure in whichone of first and second transmission lines is aligned inside the regionbetween the first and second conductive plane 1 and 2, and the other isaligned outside the region, wherein the second transmission line iselectrically connected to the first conductive plane 1 via a firstconductive via, and the first transmission line is electricallyconnected to the second conductive plane 2 via a second conductive via.

FIG. 18 shows the fifth embodiment including the first and secondtransmission lines 304A and 304B both having linear shapes, which can bevaried in various manners similar to the foregoing embodiments. Forexample, it is possible to employ spiral shapes as shown in FIG. 20.

Both the first and second transmission lines 304A and 304B are notnecessarily formed in the same shape; hence, it is possible to createcombinations in which one transmission line has a linear shape whileanother transmission line has a spiral shape, for example.

The fifth embodiment is not necessarily applied to the tetragonallattice and is thus applicable to other types of lattices as well.

6. Sixth Embodiment

Next, a sixth embodiment of the present invention will be described withrespect to a printed-circuit board with reference to FIGS. 21 and 22.

FIG. 21 is a plan view of the printed-circuit board according to thesixth embodiment, and FIG. 22 is a cross-sectional view taken along lineC-C in FIG. 21.

The sixth embodiment is directed to a printed-circuit board 50incorporating the aforementioned EBG structure. Specifically, theprinted-circuit board 50 shown in FIGS. 21 and 22 includes a groundplane 51, a power-supply plane 52, a device 53 serving as a noisesource, a device 54 sensitive to noise, and an EBG region 55 laidbetween the devices 53 and 54. As shown in FIG. 22, both the device 53serving as the noise source and the device 54 sensitive to noise areconnected to the ground plane 51 and the power-supply plane 52. Theground plane 51 and the power-supply plane 52 form a parallel-platewaveguide. In conventional printed-circuit boards, noises generated bynoise-source devices propagate through parallel-plate waveguides so asto affect noise-sensitive devices, thus causing operational errors. Theprinted-circuit board 50 of the sixth embodiment shown in FIG. 21 ischaracterized in that the EBG region 55 corresponding to theaforementioned EBG structure is disposed to cut off a noise propagationpath, thus suppressing propagation of noise between the devices 53 and54. Thus, it is possible to reduce operational error occurring in thenoise-sensitive device 54.

The printed-circuit board 50 of FIG. 22 employs the EBG structure of thefirst embodiment, which can be replaced with the EBG structures of theother embodiments.

FIG. 21 shows that the EBG region 55 is arranged in a band shape;however, it is possible to employ any type of arrangements which can cutout the noise propagation path. It is possible to arrange the EBGstructure surrounding the noise-sensitive device 54 as shown in FIG. 23.

The sixth embodiment is directed to the EBG structure installed in theprinted-circuit board 50; but this is not a restriction. It is possibleto install the aforementioned EBG structure in package substrates ofdevices or the like.

7. Seventh Embodiment

Next, a printed-circuit board according to a seventh embodiment of thepresent invention will be described with reference to FIG. 24.

FIG. 24 is a plan view of the printed-circuit board 50 according to theseventh embodiment, wherein parts identical to those of the sixthembodiment are designated by the same reference numerals, thus avoidingduplicate descriptions thereof.

The printed-circuit board 50 of the seventh embodiment includes aplurality of waveguide structures using open-end transmission lineshaving different lengths, wherein these waveguide structures are shiftedin terms of band gaps.

Similar to the sixth embodiment, the printed-circuit board 50 of theseventh embodiment includes the ground plane 51, the power-supply plane52, the device 53 serving as a noise source, and the noise-sensitivedevice 54. The seventh embodiment is characterized in that a first EBGstructure 56 and a second EBG structure 57 are formed in the EBG regionfor cutting off the noise propagation path, thus suppressing propagationof noise between the devices 53 and 54. Herein, the first EBG structure56 and the second EBG structure 57 are aligned in parallel in the noisepropagation direction. The first EBG structure 56 and the second EBGstructure 57 use respective open-stub transmission lines of differentlengths so that they differ from each other in terms of frequency bandsof band gaps. The lengths of transmission lines are set in such a waythat band gaps cause by the first EBG structure 56 are deviated fromband gaps caused by the second EBG structure 57; thus, it is possible toachieve “broad” band gaps, which cannot be obtained by a single EBGstructure, by way of the EBG region 55.

FIG. 25 shows a first variation of the seventh embodiment in which firstEBG structures 156 and second EBG structures 157 are alternately alignedin a stripe manner in the noise propagation direction.

FIG. 26 shows a second variation of the seventh embodiment in which thefirst EBG structures 156 and the second EBG structures 157 in acheckered pattern (or in checkers).

Both variations of the seventh embodiment achieve broad band gaps withthe EBG region 55.

In this connection, it is possible to employ other types of arrangementsin which the first and second EBG structures are intermixed together.Band gaps can be further enlarged by intermixing various types of EBGstructures with deviated band gaps.

Lastly, it is apparent that the present invention is not limited to theabove embodiments, but may be modified and changed without departingfrom the scope and spirit of the invention.

What is claimed is:
 1. A waveguide structure, comprising: a firstconductive plane continuously laid out in a predetermined area; a secondconductive plane laid in parallel with the first conductive plane; and aplurality of unit structures, each of which includes: a transmissionline having an open end, which is formed in a different layer from thefirst conductive plane and the second conductive plane and is positionedto face the second conductive plane; and a conductive via electricallyconnecting the transmission line to the first conductive plane, theconductive via connected to the transmission line at an end of the thinshape opposite the open end, wherein the unit structures arerepetitively aligned in a one-dimensional manner or in a two-dimensionalmanner over the predetermined area, and wherein the transmission line isformed inside a region circumscribed between the first conductive planeand the second conductive plane.
 2. The waveguide structure according toclaim 1, the transmission line having a straight, curved, or polygonalshape that is coupled with the conductive via, thereby forming amicrostrip line that uses the second conductive plane as a return path.3. The waveguide structure according to claim 1, wherein at least amajority of the plurality of transmission lines of the plurality of unitstructures have a linear shape inclined to a reference line connectingbetween adjacent ones of conductive vias with a prescribed angle thatpermits the antenna to pass between adjacent conductive vias.
 4. Thewaveguide structure according to claim 1, wherein the transmission lineshave a spiral shape.
 5. The waveguide structure according to claim 1,wherein the transmission lines have a meandering shape.
 6. The waveguidestructure according to claim 1, the transmission line having a thinshape, in a plan view, a length of the thin shape being adequate tocause a line-length resonance to occur solely in a length direction ofthe transmission line
 7. The waveguide structure according to claim 1,as implemented in a printed-circuit board.
 8. The waveguide structureaccording to claim 7, wherein the printed-circuit board includes aplurality of different areas of the waveguide structure.
 9. Thewaveguide structure according to claim 8, wherein the plurality ofdifferent areas provide respective band gaps of different frequencybands.
 10. The waveguide structure according to claim 1, wherein thetransmission line formed inside the region between the first and secondconductive planes comprises a first transmission line, and wherein theconductive via electrically connecting the first transmission line tothe first conductive plane comprises a first conductive via, the unitstructures of the waveguide structure further comprising: a secondtransmission line having an open end laid on a second plane, which ispositioned to face the second conductive plane outside a regioncircumscribed between the first and second conductive planes; and asecond conductive via electrically connecting the first transmissionline to the second transmission line, wherein a clearance is formed at aprescribed position corresponding to the second conductive via in thesecond conductive plane, which is thus electrically isolated from thesecond conductive via.
 11. The waveguide structure according to claim10, wherein each of the first transmission line coupled with the firstconductive via and the second transmission line coupled with the secondconductive via forms a microstrip line using the second conductive planeas a return path, and wherein each transmission line has one open endand the other end connected to its conductive via.
 12. The waveguidestructure according to claim 10, further comprising: a thirdtransmission line, which is formed in a third plane positioned betweenthe first conductive plane and the first transmission line so as to facethe first conductive plane; a fourth transmission line having an openend, which is formed in a fourth plane positioned to face the firstconductive plane outside a region circumscribed between the first andsecond conductive planes; and a third conductive via electricallyconnecting the third transmission line to the fourth transmission line,wherein a first clearance is formed at a first position corresponding tothe third conductive via in the first conductive plane, which is thuselectrically isolated from the third conductive via.
 13. A waveguidestructure, comprising: a first conductive plane continuously laid out ina predetermined area; a second conductive plane laid in parallel withthe first conductive plane; and a plurality of unit structures, each ofwhich includes: a first transmission line having an open end, which isformed in a first plane different from the first conductive plane andthe second conductive plane and positioned to face the first conductiveplane; and a second transmission line having an open end, which isformed in a second plane different from the first conductive plane andthe second conductive plane and positioned to face the second conductiveplane, wherein the unit structures are repetitively aligned in aone-dimensional manner or in a two-dimensional manner.
 14. The waveguidestructure of claim 13, further comprising a conductive via in each unitstructure that electrically connects the first transmission line to thesecond transmission line.
 15. The waveguide structure of claim 13,further comprising: a first conductive via electrically connecting thesecond transmission line to the first conductive plane; and a secondconductive via electrically connecting the first conductive plane to thesecond conductive plane, wherein a first clearance is formed at a firstposition corresponding to the second conductive via in the firstconductive plane, which is thus electrically isolated from the secondconductive via, and wherein a second clearance is formed at a secondposition corresponding to the first conductive via in the secondconductive plane, which is thus electrically isolated from the firstconductive via.
 16. The waveguide structure according to claim 13,wherein the first transmission line coupled with the conductive viaforms a microstrip line using the first conductive plane as a returnpath, and wherein the second transmission line coupled with theconductive via forms a microstrip line using the second conductive planeas a return path.
 17. The waveguide structure according to claim 13,wherein at least one of the first transmission line and the secondtransmission line is aligned outside a region circumscribed by the firstconductive plane and the second conductive plane, and wherein aclearance is formed at a prescribed position corresponding to theconductive via in the at least one of the first conductive plane and thesecond conductive plane, which is thus electrically isolated from theconductive via.
 18. The waveguide structure according to claim 13, asimplemented in a printed-circuit board.
 19. The waveguide structureaccording to claim 13, wherein the plane of the first transmission lineis positioned between the first conductive plane and the secondconductive plane, and wherein the plane of the second transmission lineis positioned outside a region circumscribed between the first andsecond conductive planes, the unit structures further comprising: athird transmission line, which is formed in a third plane positionedbetween the first conductive plane and the first transmission line so asto face the first conductive plane; a fourth transmission line having anopen end, which is formed in a fourth plane positioned to face the firstconductive plane outside a region circumscribed between the first andsecond conductive planes; a second conductive via electricallyconnecting the first transmission line to the second transmission line;and a third conductive via electrically connecting the thirdtransmission line to the fourth transmission line, wherein a firstclearance is formed at a first position corresponding to the thirdconductive via in the first conductive plane, which is thus electricallyisolated from the third conductive via, and wherein a second clearanceis formed at a second position corresponding to the second conductivevia in the second conductive plane, which is thus electrically isolatedfrom the second conductive via.
 20. The waveguide structure according toclaim 15, wherein each of the first transmission line and the secondtransmission line both coupled with the second conductive via forms amicrostrip line using the second conductive plane as a return path, andwherein each of the third transmission line and the fourth transmissionline both coupled with the third conductive via forms a microstrip lineusing the first conductive plane as a return path.